The energy consumption of Heating, Ventilation, and Air Conditioning (HVAC) systems in buildings accounts for almost half of the total energy usage. Therefore, research on HVAC energy management is essential. Prediction of indoor temperature and relative humidity is crucial in the field of efficient building energy management. However, this task is challenging due to the complex spatial-temporal coupling features and multivariable dependencies. To address these issues, we propose a multitask learning model called the Spatial-temporal Convolutional Multitask Deep Learning (STCMT) model for predicting the temperature and relative humidity in multi-zone buildings. This model utilizes Spatial-temporal Convolutional Block (ST-Conv block) to extract the spatial-temporal features of the variables in HVAC systems. Additionally, to address intervariable dependencies, we utilize the Transformer Model to capture the interrelationships among different variables. The proposed model has been implemented on a smart building dataset, and the results indicate that the proposed method outperforms other methods in indoor temperature and relative humidity prediction, including Support Vector Regression (SVR), Long Short-Term Memory (LSTM), MultiDeT, and Graph WaveNet.